Solve for x 81^(3x-6)=729^(x+3)

$81^{3 x - 6} = 729^{x + 3}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$9^{2 (3 x - 6)} = 9^{3 (x + 3)}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 (3 x - 6) = 3 (x + 3)$

Step 3

Solve for $x$ .

Simplify $2 (3 x - 6)$ .

Rewrite.

$0 + 0 + 2 (3 x - 6) = 3 (x + 3)$

Simplify by adding zeros.

$2 (3 x - 6) = 3 (x + 3)$

Apply the distributive property.

$2 (3 x) + 2 \cdot - 6 = 3 (x + 3)$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 6 = 3 (x + 3)$

Multiply $2$ by $- 6$ .

$6 x - 12 = 3 (x + 3)$

Simplify $3 (x + 3)$ .

Apply the distributive property.

$6 x - 12 = 3 x + 3 \cdot 3$

Multiply $3$ by $3$ .

$6 x - 12 = 3 x + 9$

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$6 x - 12 - 3 x = 9$

Subtract $3 x$ from $6 x$ .

$3 x - 12 = 9$

Move all terms not containing $x$ to the right side of the equation.

Add $12$ to both sides of the equation.

$3 x = 9 + 12$

Add $9$ and $12$ .

$3 x = 21$

Divide each term in $3 x = 21$ by $3$ and simplify.

Divide each term in $3 x = 21$ by $3$ .

$\frac{3 x}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{21}{3}$

Divide $x$ by $1$ .

$x = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$x = 7$

Solve for x 81^(3x-6)=729^(x+3)

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